What is the integral from 4 to 7 of x^3ln(4x) ?

The integral from 4 to 7 of x^3ln(4x) is -256ln(2)-2145/16+2401/4 ln(28)

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integral from 4 to 7 of x^3ln(4x)

\int_{4}^{7} x^{3} ln (4 x) d x

- 256 ln (2) - \frac{2145}{16} + \frac{2401}{4} ln (28)

Decimal Notation

1688.64757 \dots

Solution steps

\int_{4}^{7} x^{3} ln (4 x) d x

Apply Integration By Parts

: [\frac{1}{4} x^{4} ln (4 x) - \int \frac{x ^{3}}{4} d x]_{4}^{7}

= [\frac{1}{4} x^{4} ln (4 x) - \int \frac{x ^{3}}{4} d x]_{4}^{7}

\int \frac{x ^{3}}{4} d x = \frac{x ^{4}}{16}

= [\frac{1}{4} x^{4} ln (4 x) - \frac{x ^{4}}{16}]_{4}^{7}

Compute the boundaries:

- 256 ln (2) - \frac{2145}{16} + \frac{2401}{4} ln (28)

= - 256 ln (2) - \frac{2145}{16} + \frac{2401}{4} ln (28)

e^{\frac{7}{u}}

\frac{d x}{d t} = x - 2

\int csc (\frac{3}{4}) x cot (\frac{3}{4}) x d x

\frac{d x}{d t} + \frac{10 x}{20000 - 5 t} = 5

n = 0 \sum \infty \frac{n ^{n}}{2 ^{n}}

What is the integral from 4 to 7 of x^3ln(4x) ?
The integral from 4 to 7 of x^3ln(4x) is -256ln(2)-2145/16+2401/4 ln(28)